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Exceptional points in lossy media lead to deep polynomial wave penetration with spatially uniform power loss



Alexander Yulaev, Sangsik Kim, Qing Li, Daron Westly, Brian Roxworthy, Kartik Srinivasan, Vladimir Aksyuk


Waves entering a spatially uniform lossy medium typically undergo exponential decay, arising from either the energy loss of the Beer–Lambert–Bouguer transmission law or the evanescent penetration during reflection. Recently, exceptional point singularities in non-Hermitian systems have been linked to unconventional wave propagation phenomena1,2, such as the predicted extremely spatially broad constant-intensity photonic guided modes3. Despite the theoretical promises for decay-free optical fields, the experimental realization of constant-intensity waves has been revealed so far only in macroscale acoustical waveguides with discrete gain-loss inclusions4. Here we discover and experimentally demonstrate deep, linear wave penetration accompanied by a striking uniformly distributed energy loss across the arbitrary thickness of homogeneous periodically structured medium with exceptional-point-containing band diagrams. Predicted by coupled mode theory and supported by fully vectorial electromagnetic simulations, hundreds-of-waves deep penetration and uniform radiation loss are experimentally observed in periodically nanostructured photonic slab waveguides. The spatially uniform, decay-free radiative energy loss is measured across the entire structured waveguide region, regardless of its length, however the optical bandwidth of the effect becomes progressively narrower for deeper penetration distances of longer waveguides. While the demonstrated photonic device finds an immediate application for generating large uniform and surface-normal free-space plane waves directly from the surface of a photonic integrated circuit, the uncovered wave propagation regime is universal and holds true across physical domains supporting wave phenomena, opening new horizons for dispersion-engineered materials empowered by exceptional point physics.
Nature Nanotechnology


exceptional points, grating waveguide, grating coupler, wave media, wave propagation


Yulaev, A. , Kim, S. , Li, Q. , Westly, D. , Roxworthy, B. , Srinivasan, K. and Aksyuk, V. (2022), Exceptional points in lossy media lead to deep polynomial wave penetration with spatially uniform power loss, Nature Nanotechnology, [online],, (Accessed June 13, 2024)


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Created April 21, 2022, Updated November 29, 2022